Continuing Education
Course
Every Pump Operator’s
Basic Equation
By Paul Spurgeon
TRAINING THE FIRE SERVICE FOR 135 YEARS
To earn continuing education credits, you must successfully complete the course examination.
The cost for this CE exam is $25.00. For group rates, call (973) 251-5055.
Every Pump Operator’s
Basic Equation
Educational Objectives
On completion of this course, students will
1. Learn how to develop a proper fire stream
3. Describe two friction loss formulas used by fire departments
2. Define friction loss and explain two ways water flows
through hoses
4. Learn how elevation must be calculated into fire stream
calculations
B Y PA U L S P U R G E O N
T
he equation EP = NP + FL + APP + ELEV is the
basic equation every pump operator needs to calculate
when operating the fire pump. Today, many pump panels have flow meters that allow the pump operator to match
the readout on the pump panel with the gallon-per-minute
(gpm) flow of the selected nozzle. This is a disservice to the
integrity of the pump operator. A knowledgeable operator
needs to understand how a proper fire stream is developed
and how each part is applied. Only with this knowledge can
the pump operator go from being a knob puller who sets
predetermined figures on a gauge to an efficient engineer capable of filling the hoselines with the proper amount of water
not only to extinguish fires but also to keep crews safe on the
fireground.
Each figure can be calculated using simple math. How the
concepts are developed is explained below. The engine pressure is calculated by plugging numbers into each figure and
adding or subtracting them.
• EP = Engine Pressure
• NP = Nozzle Pressure
• FL = Friction Loss
• Elev = Elevation Loss or Gain
• App = Appliance Friction Loss
Some figures may be used more than once; others may not
be used at all. If more than one size of hose is used, you will
have to figure friction loss for each size. This also applies if
multiple appliances are used or if hoselines are laid both up
and down a hill. The pump operator needs to account for
each of these figures each time a hoseline is pulled from the
apparatus.
NOZZLE PRESSURE
To be called a fire stream, a hoseline needs to have a nozzle
attached to its end. This nozzle gives the stream its shape,
reach, and velocity. By definition, a fire stream is a stream of
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water after it leaves the nozzle until it reaches its final destination, which is usually the seat of the fire. As the streams are
being produced, they are affected by the discharge pressure,
nozzle design, and nozzle setting. A discharge pressure that is
too strong not only will be very hard to handle but will also
break up into smaller droplets, which aren’t as effective in
extinguishing the fire. A discharge that is too weak may not be
delivering enough gpm to overcome the British thermal units
(Btus) being produced by the fire. An adequate stream also
needs to have the reach to be able to hit the seat of the fire.
After the water leaves the nozzle, the stream is also affected
by nature in the forms of gravity and wind. The stream needs
to be strong enough to overcome these factors. There has to
be enough reach so the firefighters don’t have to be in the
absolute hottest environment. If the stream falls short of the
fire, it cannot extinguish the fire. If the stream isn’t capable
of overcoming the wind, it may not be possible to place the
water on the seat of the fire, where it is needed.
Standard Pressures
The fire service uses three standard nozzle pressures. These
standards are derived from years of trial and error and experience. The nozzle pressure can be adjusted upward to deliver
more gpm flow or downward to make the line more maneuverable. Unfortunately, we can’t have both. If the nozzle pressure
is increased, a few more gpm can be delivered, but the hoseline
will become stiffer and harder to handle. There is even a point
where the pressure becomes so great that the turbulence in
the stream prevents the producing of a working fire stream. If
the nozzle pressure is decreased, the hoseline will be easier to
handle but at the expense of lower gpm. The standards give
a good compromise for delivering the best of both worlds. To
extinguish the fire while being able to maneuver the hoseline,
the following nozzle pressures have been adopted:
• Smooth bore handline: 50 pounds per square inch (psi).
• Fog nozzle handline: 100 psi.
• Smooth bore master stream: 80 psi.
pump op equation ●
These standards give us a good basic starting point in figuring the overall engine pressure.
Smooth Bore Nozzles
A smooth bore nozzle is simply a tube that narrows down
to an opening with a specific inside diameter. As the water
gets narrowed through the nozzle, it develops its smooth solid
stream. In the late 1890s, John R. Freeman1 conducted experiments designed to define what a good solid stream is. He
came up with four requirements that are still used today:
A stream that has not lost its continuity by breaking into
showers or a spray.
A stream that shoots nine-tenths of the whole volume of
water inside a 15-inch-diameter circle and three-fourths of
its volume into a 10-inch-diameter circle at its break-over point.
A stream stiff enough to attain, under fair conditions, the
named height or distance, even through a breeze.
A stream that, with no wind blowing, will enter a room
through a window and strike the ceiling with enough
force to splatter well.
These standards give a good foundation for building a good
quality fire stream.2
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Discharge
As we know, it is not the pressure of a stream that extinguishes a fire but the amount of water in gpm that cools a fire.
The officer in charge of a fire needs to determine the amount
of water needed to extinguish the fire and choose the appropriate hoseline and nozzle that will deliver the correct gpm. Large
fires make for good news coverage, but in reality they happen
because the firefighters were unable to place enough water at
the seat of the fire to overcome the Btus being produced. The
officer as well as the pump operator need to know the gpm
flow from different nozzle tips to know how much fire each
can extinguish. As a general rule, the maximum nozzle diameter
should not exceed one-half of the size of the hose to which it
is attached—for example, a 2½-inch handline should not have a
smooth bore nozzle any larger than 1¼ inches. A 1¾-inch handline should have a nozzle tip no larger than 7⁄8 inch.
The amount of water discharging from a smooth bore is
determined by the nozzle pressure and the inside diameter of
the opening. The formula for determining the gpm flow from
a smooth bore nozzle is as follows:
29.72D2√P (D = nozzle diameter; √P = square root of pressure)
For example, a one-inch smooth bore tip will have a discharge of 210 gpm: 29.72 × 12 × 7.07 = 210 gpm.
Fog Nozzles
Many fire departments have chosen to place combination
fog nozzles on their apparatus. They feel that it is important
to have the option of delivering a stream that can be adjusted
from a straight stream to a wide fog pattern. Many officers
and nozzle operators like having the flexibility a fog nozzle
provides. This nozzle is also good for auto fires, other outside
fires, and liquid petroleum fires.
Table 1. Expansion and Temperature
Temperature (ºF)Expansion Ratio
212º
1,700 to 1
500º
2,400 to 1
1,200º
4,200 to 1
Figure 1. Laminar Flow
Figure 2. Turbulent Flow
Note that I did not say solid stream when referring to
the pattern setting. At the narrowest pattern, a fog nozzle
still produces a fog stream. It consists of tiny water droplets
discharged in a uniform direction toward the fire. The small
water droplets, if applied properly, will absorb the heat faster
than a solid stream. This is because there is more surface
area with all of the droplets compared with a solid stream.
Another advantage of having tiny water droplets is that they
quickly turn into steam. When a fire is in an enclosed space, a
relatively small amount of fog stream can be shot into the area
(the area is sealed tight), and the water will turn into steam
smothering the fire. This is called the indirect attack method.
Its advantage is that it uses relatively small amounts of water.
This helps in preventing water damage to the structure. This
method of attacking fire was first developed by Chief Lloyd
Layman while he was in the U.S. Coast Guard. When water
turns to steam, it expands. The amount of expansion is determined by the amount of heat in the room.
Note: The indirect attack is used only in enclosed spaces
where there is no possibility of life in the room. The steam will
burn and kill anyone inside the environment. If there is a possibility that someone is in the room, including firefighters, use a
fog pattern in conjunction with proper ventilation. As the water
is turned into steam, it will cool the burning material, but the
steam has to be allowed to escape to the outside. A close-up
fire attack must be coordinated with proper ventilation. Table 1
shows the amount of expansion at various temperatures.
FRICTION LOSS
In the fire service, friction loss is defined as the loss of
energy in pressure whenever water runs through hoses,
fittings, and appliances. As water runs through hose, it rubs
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against the lining of the hose, the couplings, and even itself.
Each time this happens, friction causes the water to slow
down. Pump operators need to compensate for this loss. As
far as pump operators are concerned, there are two ways
water flows through hoses. The first is laminar flow, which
occurs with relatively low velocities. In a perfect world, the
water would flow right through the hose and never encounter any obstacles to slow it down. In laminar flow, the water
flows in parallel lines with the flow at the center moving at
a greater velocity than at the edges and decreases further
out toward the edges of the hose. Picture layers of water
flowing on top of each other. In laminar flow, the layers
move smoothly against each other all in one direction.
The second type of flow is “turbulent.” As stated before,
as the water flows through the hoses and appliances, it rubs
against the lining of the hose and appliances, causing friction.
It also flows over couplings and around bends in the hose,
causing friction. Picture a single drop of water inside the hose.
As it flows along, it contacts the lining, a coupling, or a bend
in the hose. As it makes this contact, it changes direction even
slightly and stops flowing in a nice straight line. This will slow
down the forward velocity of the droplet. This is the simplest
explanation of friction loss. Every time the water changes
direction for any reason, friction is created.
Friction is also caused by the water itself. As a liquid flows
past itself, it creates friction with the layers next to it. As
each layer comes in contact with another layer, it moves and
changes direction. This causes the velocity to slow down. A
good example of this can be seen when pouring very thick
syrup down a gentle slope. If you watch the front end of
the syrup, it will look as if it is rolling down the slope. Each
layer seems to grab the layer next to it and pulls it along.
Water does the same thing. As it flows through the hose,
it rubs and pulls and moves in directions other than the
straight line we want.
A simple way of demonstrating this principle is to turn on
your garden hose. Without connecting a nozzle to the end,
place the hose in a straight line. The water coming out the
end runs in a nice smooth stream. Immediately at the end
of the hose, the water has a nice solid cylindrical shape.
Now slightly kink the hose about 12 to 18 inches behind the
discharge opening. You now see not only that the stream has
lost its forward velocity but also that the shape of the stream
isn’t nearly as uniform as before. This is a very simplified
version of what happens inside a fire hose.
Friction loss in fire hose is governed by the following rules:
Friction loss varies with the quality of the hose. The
thickness of the inner lining, the age of the hose, and the
weave of the jacket all affect the quality of the hose. Even with
the advancement in the quality of the inner lining of the hose,
some friction still exists. It is impossible to have a perfectly
smooth inner lining. Every little imperfection in the lining will
create friction.
Friction loss varies directly with the length of the
hose. Friction loss is calculated in 100-foot lengths;
the total friction loss is figured when all lengths are added
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2
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together. For example, if the friction loss in one length of
1¾-inch hose is 15 psi, then if four 100-foot lengths are added
together, the total friction loss would be 60 psi.
Friction loss varies with the square of the velocity. If the
velocity is doubled, the friction loss is quadrupled. If the velocity is quadrupled, the friction loss will be increased 16 times.
For a given flow, the friction loss varies inversely
as the fifth power of the diameter of the hose. This
is the most important thing to understand when limiting the
effects of friction loss. This rule shows why it is important to
increase the diameter of the hose when trying to keep friction loss to a minimum. While keeping the flow the same, as
the hose size is doubled, the friction loss is only (½)5 or 1⁄32
times the friction loss in the smaller hose. This is the reason
many fire departments switched from 1½-inch hose to 1¾inch hose. This is illustrated as follows:
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1.75 ÷ 1.5 = 1.167 = 2.16
This shows that the friction loss in 1¾-inch hose is half of
that for a 1½-inch hose. A 1¾-inch hose isn’t any more difficult to handle than the smaller 1½-inch hose and has much
less friction loss, but it can deliver a larger volume of water at
the same pressure.
For a given velocity, friction loss is independent of
the pressure. The amount of friction loss in a hose depends on the amount of water flowing through the hose and
the velocity at which it is moving. If the hoseline is laid up a
hill, the pump will need to overcome the back pressure created by the elevation, but the friction loss would remain the
same. If the friction loss in 100 feet of 2½-inch hose is 15 psi,
the pressure in the hoselay would decrease by 15 psi for every
100-foot length connected, but the pump discharge pressure
will need to be increased to compensate for the elevation loss.
5
The Friction Loss Formula
As stated before, there are many factors that affect how
much friction loss there might be in a given length of hose.
It is nearly impossible to tell the condition of the lining, for
example. The only true way to figure the amount of friction
loss is to connect pressure gauges to each end of the hoseline, place the hoses in straight lines and on level ground, and
subtract the difference. It is important to keep the hose and
equipment in good working condition at all times to eliminate
as much of the friction-causing problems as possible.
For many years, certain formulas have been used to get a
fairly accurate measurement of the friction loss. These formulas are not perfect, but they are adequate for the fire service.
Underwriters’ Formula
The most widely used formulas for determining friction loss
in a single 2½-inch hoseline are the following:
FL = 2Q2 + Q and FL + 2Q2 + ½Q
These formulas are called the “Underwriters’ formulas.” The
first is used when the gpm flow is 100 gpm or higher. The
second formula is used for flows lower than 100 gpm.
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Table 2. Hose Size and
Conversion Factor
Hose
Factor
1½-inch
12.99 or 13
1¾-inch
5.98 or 6
2-inch
3.05 or 3
3-inch
2.49 or 2.5 (divide)
Table 3. Hose Size and Coefficient
Hose Size
1¾-inch
2½-inch
3-inch
4-inch
5-inch
Coefficient
15.50
2.00
.80
.20
.08
In calculating these formulas, start by knowing how many
gpm of flow you have based on the nozzle tip size. Divide the
gpm figure by 100 to give you “Q.”
Q = gpm /100
Example: Q = 400 gpm /100 = 4
When calculating friction loss for hose sizes other than 2½ inch,
you must use a conversion factor. You calculate the factor by using
friction loss rule #4, which states: “If the flow stays the same, the
friction loss varies inversely as the fifth power of the diameter of the
hose.” Table 2 shows the conversion factor for different hose sizes.
Multiply or divide the formula by the conversion factor to get
the correct friction loss.
Coefficient Formula
Another formula used by some fire departments is “CQ2L.”
Some believe this formula is easier to use, but the operator
needs to remember the coefficient for each hose size.
C = Coefficient
Q = Gpm/100
L = Length in 100 feet
A coefficient is a number used for a specific hose size. Table
3 shows various hose sizes and their coefficients.
When comparing calculations of each of the two formulas,
you will notice the answers are slightly different. Which formula
is correct? The answer is “both.” There is no right or wrong
formula; fire departments use either formula. As stated before,
there are too many factors involved to accurately calculate a
friction loss. The only way to accurately figure the friction loss
in any length of hose is to place pressure gauges on each end
of the line and subtract the difference. The important thing is to
work with both formulas and see which works best for you.
Combination Layout
Until now we have discussed only single hoseline layouts;
single lines are easy to figure. You only need to figure one
friction loss and apply it to the overall formula. But what hap-
pens when there is a combination layout?
A combination layout consists of multiple hoselines that
combine into one or one hoseline that divides into more than
one line. The most common combination layout consists of
multiple lines that combine into one.
These layouts are used any time more water is needed at
the nozzle than can be easily delivered through any one hoseline. For example, when very long hose stretches are needed,
there would be too much friction loss in one single hoseline,
so it is divided among two or more lines and then connected
with a siamese into the attack line. Another situation is supplying a standpipe or a sprinkler connection on a building.
Two or more hoselines are connected at the building and then
one internal pipe carries the water to where it is needed.
The most efficient way of calculating this type of layout is to
break the layout down into separate parts.
It is best to separate the attack line first. We know that a
one-inch tip flows 210 gpm. Using that, we can figure the
friction loss for this section: 2Q2+Q × L = 21.84.
Next, figure the friction loss in the two lines supplying
the attack line. Divide the total gpm (210) by the number of hoselines (2), and figure the friction loss for one of the
lines. The other line will be the same. Each hoseline carries
half of the total flow: 2(1.052) + 1.05 × L = 9.25. Don’t add
9.25 twice. You need to figure and add it only once. Even if
there are five supply lines, figure the friction loss for one line,
and add it only once.
Note: If the hoselines that are going to be split are two different lengths, average the two. If at all possible, it would be
better to change the lines so they are the same length. It is
also best if the same size hoselines are used. This makes the
calculations reasonably easy to figure.
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Other Applications Using the Siamese
The siamese is used to convert multiple hoselines into one
line when supplying a standpipe or a sprinkler connection.
Multiple lines connect to the building and supply attack lines
or sprinkler heads. The siamese is used also when an engine
needs to supply a ladderpipe on an aerial ladder. The mistake
many people make is not to divide the gpm among however
many supply lines there are. If the total flow is not divided
among the separate lines, the calculations will be way too high.
Wyed lines take special considerations. The same principle
applies when a supply line is split into two attack lines: Each
section needs to be figured separately, but it is extremely
important that each attack line be the same as the other. Each
needs to be the same diameter hose and the same length, and
each needs to flow the same gpm from the nozzle. If the attack
lines are different, the friction loss will be different in each line,
and it will be impossible to correct overall friction loss.
Example: The friction loss for the supply line is 30 psi. One
attack line is 200 feet of 1¾-inch hose with a 200-gpm fog
nozzle. The friction loss for this hoseline is 120 psi.
The second attack line is 200 feet of 1¾-inch hose with a
100-gpm fog nozzle. The friction loss for this hoseline is 36 psi.
If the 200-gpm nozzle is supplied properly, the total friction
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loss would be 150 psi. There is no possible way of supplying
the second line with the proper 66 psi. It is not physically possible to pump two separate pressures through one hoseline.
Another situation where more than one friction loss needs to
be figured is when very long hoselays are needed. For example,
an engine is pumping while at a hydrant, and the fire is a long
distance away. The best thing to do is to pump through largerdiameter hose up to the fireground and then have a shorter
attack line that is smaller in diameter and easier to maneuver.
Question: What is the total friction loss in 700 feet of threeinch hose reduced to 200 feet of 1¾-inch attack line with a
one-inch straight tip?
Answer: Figure the attack line first:
2 × 2.12 + 2.1 × 2 × 6
65.52 × 2 (length)
= 131.04 psi
Table 4. Friction Loss
and Appliances (Denver Fire Department)
Appliance
Siamese
Wye
Bresnan Distributor (1¾-inch)
Bresnan Distributor (2½-inch)
Multiversal
Deck Gun
Ladderpipe
Standpipe System
Friction Loss
5 psi
5 psi
3 psi
5 psi
10 psi
10 psi
15 psi
25 psi
memorize whichever formula your department uses as well as
the friction loss rules and how they are applied.
Next, figure the three-inch hose:
2 × 2.12 + 2.½.5
4.37 × 7 (length)
= 30.59 psi
Finally, add the two together: 131.04 + 30.59 = 161.63 psi.
As you can see, if the entire hoseline were 900 feet of 1¾inch hose, the friction loss would be 589.68 psi. A pressure
this high would be very hard on the pumps and certainly
would burst the hose. That is the reason it is so important to
pump through a larger-diameter hoseline for all the distance
except for the attack line.
When you are on the scene of a twoalarm fire, the pump operator doesn’t
have time to figure friction loss for every
hoseline. Most fire departments calculate
the friction loss for the hoses and nozzles
they carry and write them on what is called
a “pump chart.” Most charts list the nozzles
on the apparatus, their gpm, and the friction
loss. The operator simply needs to look at
the chart and start adding the figures. This
makes it much easier and quicker on the
fireground where time is critical.
Friction loss happens every time
water flows through hoses, pipes, or appliances. Every time a hoseline is pulled,
the pump operator needs to account
for it to give the nozzleman the proper
amount of water to extinguish the fire.
It is the pump operator’s primary responsibility to get the calculations right
and supply the hoseline with the proper
pressure and flow rate. Improper calculations can create dangerous situations
for the crews inside the fire area. Too
low of a pressure will create a situation
where there is not enough water to extinguish the fire; too high a pressure can
possibly injure the fire crews inside the
building. When calculating friction loss,
APPLIANCE FRICTION LOSS
In the above section, appliances such as wyes, siameses,
and reducers were never figured into the friction loss calculations. They are so special that they get their own calculation in
the overall equation. Appliances are devices designed to work
in conjunction with hoses to help deliver the water. They are
designed to be placed in the middle or at the end of a hose
layout to deliver the water. Even fire department connections
for standpipes are considered appliances. Ladderpipes on
aerial trucks are considered appliances. Appliances can be
used to combine or divide hoselines
or to help deliver the water to where it
needs to go.
Every water appliance used in the fire
service, from a simple wye to a ladderpipe, has friction loss. The manufacturers
of these appliances work hard to keep
the amount of friction loss to a minimum
but, as noted before, each time the water
moves or changes direction, friction is
created. Each engine company should
keep track of what appliances are on
the rig and who makes them. If manuals
are not available, go to the Web site or
contact the company and learn as much
about each one as possible. There are
lists and charts diagramming the friction
loss for given flows.
Just as with hoselines, every time
water changes direction, more friction
loss is created. As the water is split, combined, or moves through the appliance,
it will change direction, which causes
friction loss. The same friction loss rules
apply. As the inside diameter increases,
the friction loss decreases. Just as the velocity increases, so does the friction loss.
Many fire departments such as the
Denver (CO) Fire Department give set
Figure 3. Elevation
from Top of Water
to Height of Outlet
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pump op equation ●
values for each appliance. These friction loss values are averages based on the flows usually associated with each appliance.
When pumping at a fire, these figures are accurate enough.
Table 4 contains the friction loss the Denver Fire Department assigns to appliances.
These are just some of the appliances in use today. Inventory your apparatus, and make sure that each piece of equipment is accounted for and the friction loss for each one is
known. Check with the manufacturer, if necessary, to determine the friction loss for each appliance.
being used. What matters is how much higher the reservoir is
than where the water is being used. A water tank raised above
the ground can supply a hydrant at ground level. The height of
the water level in the tank will determine the pressure found at
the hydrant. The formula for determining pressure when head
is known is pressure (P) = 0.434 × head (H).
Question: The surface of the water in a gravity tank is 134
feet above a hydrant. What will be the static pressure on the
hydrant created by head?
ELEVATION
Elevation is the last calculation we need to make to finish the equation. In firefighting terms, elevation is pressure
created by gravity. Unless the hoselines are laid on perfectly
flat ground, you need to adjust for elevation. Many times, the
elevation change is minimal, but the pump operator needs to
be aware at all times. In many municipalities, a house will sit
higher than the street. Take a look at the driveway and note
if there is a slope to it. This pressure needs to be calculated
when moving both up and down in elevation. At times, the
hoseline is pulled up a hill and then down the other side.
Other times, the hoselines are laid on flat ground into standpipe connections, but the attack line is being used on an upper floor of the building. Every time water is moved higher
or lower than the pump, you need to make adjustments.
The downward pressure of a liquid is directly proportional to
its depth. A one-inch by one-inch column of water standing one
foot tall will have a pressure at its base of 0.434 pounds. The
pressure will increase by 0.434 pound for every foot added to
the height. The pump operator needs to adjust for this pressure.
HEAD PRESSURE
“Head” refers to the vertical distance from the top of the water to where it is being used. The amount of pressure created
by gravity depends on the height of the level of the water in
comparison to where it is being used. For example, a column
of water 50 feet tall will create a pressure of 21.7 pounds at its
base. The opposite is also true. If 21.7 pounds of pressure are
applied to the base of the column, the water will rise 50 feet.
Determining the Pressure
When the Head Is Known
Before mechanical pumps were used on water distribution
systems, gravity was used to increase pressure. Water tanks
were placed on buildings and towers to deliver water to sprinkler systems and hydrants. These tanks were placed at varying
heights according to how much pressure was needed. A reservoir high in the mountains can deliver the pressures needed
to supply a city below. Cities such as Denver are fortunate to
have tall mountains full of reservoirs close by. The reservoirs
fill up with water as the snow melts, and the cities below use
what they need throughout the year. It is all gravity fed, allowing nature to take care of the cities below. Even though the
reservoir may be miles away, the only thing that matters is the
vertical distance between the reservoirs and where the water is
Answer: P = .434H
P = (.434) (134)
H = 134 feet
P = 58.16 psi
Overcoming Head Pressure
The examples have shown only head pressure moving toward
the ground from an elevated height. Head also applies in elevation.
When hoselines are placed up a hill or into a building, a pumper
is needed to overcome the pressure caused by head. Every time a
pump operator pumps into a standpipe connection on a building,
he needs to make an elevation calculation. In many jurisdictions,
this happens many times a day. The same formula applies; only
the pump operator needs to add this pressure to the formula. If a
nozzle operator is 40 feet up a hill, the pump operator needs to
add pressure to overcome the head pressure working against the
pump. This pressure is called “back pressure.”
P = H × 0.434
P = 40 × 0.434 = 17.36 psi
Question: What would be the back pressure when pumping
up a 35-foot hill?
Answer: P = H × 0.434
P = 35 × 0.434 = 15.19 psi
The pump operator needs to add this pressure to the calculation.
If the nozzle were 40 feet down a hill, the pump operator
would need to subtract the pressure. This pressure is called “forward pressure.”
P = H × 0.434
P = -40 × 0.434 = -17.36 psi
Sometimes the lines aren’t laid so easily up or down a hill. Many
times, the hose travels down a hill and back up another hill. The
pump operator simply needs to find the difference. For example, if
the hoseline is pulled up a 30-foot hill then down the other side a
total of 20 feet, the operator needs to adjust for a rise of 10 feet.
P = H × 0.434
P = (30 – 20) × 0.434
P = 10 × 0.434
P = 4.34 psi
In this case, 4.34 psi needs to be added to the calculation because the final height is above the level of the pump. In mountain areas, the pump operator finds this a common occurrence.
Most of the time, trying to figure the overall elevation change
becomes a guessing game. The easiest way is to figure a starting
point and an ending point and calculate the difference. One of
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the first fires I pumped at happened to be a situation like this.
When I looked, the terrain dropped down to the entrance of the
building, but the fire was on the third floor. As I looked across, it
became clear that the fire was on the same plane I was on. This
made for an elevation change of zero. So even though there were
two elevation changes, the end result turned out to be zero.
The same formula applies when pumping into a building. The
only difference is that we don’t account for the height of the first
floor because the fire department connection is usually about the
same distance from the ground as the standpipe connection is
from the fire floor. For example, a fire is on the seventh floor of
a building in which each floor is 10 feet tall. We need to account
for only six floors or 60 feet.
P = H × 0.434
P = 60 × 0.434
= 26.04 psi
Question: What is the elevation pressure when pumping
into a 35-story high-rise building that has a fire on the 27th
floor? Assume each floor is 10 feet tall.
Answer: P = H × 0.434
P = 26 × 0.4
Question: A fire is on the 14th floor of an office building.
The pumper sits on a hill 30 feet above the fire department
connection. What is the head, and what is the pressure because of elevation? Do we need to add or subtract the pressure from the calculation? Assume 10 feet per floor.
Answer: Up 130 feet minus 30 feet down = 100 feet total
elevation change.
Elev = 130 – 30 = 100
Back Pressure (BP) = 100 * 0.434 = 43.4 psi
We need to add this pressure because the nozzle is above
the level of the pump.
PUTTING IT ALL TOGETHER
Now that each part of the formula has been explained, you
can put it all together. The easiest way to start is to write down
the formula. Some people find it easier to draw a diagram of
the hose layout to help visualize each part of the problem.
Remember that each part may be used more than once.
There may be different sizes of hose or multiple appliances.
Even if one or more parts of the formula are not used, it is
always a good idea to write down the abbreviation anyway. All
that is needed is to place a zero in its place. Many people find
that starting with the nozzle and working backward is the best
way to keep everything straight. Follow the water backward,
and fill in the numbers into each spot.
In master stream operations, which use large volumes of water,
every part of the formula is used. Generally, master streams are
used when the volume of flow is higher than 350 gpm. Monitors,
deck guns, elevated platforms, and ladderpipes are considered
master streams. Even though large volumes of water are used,
the same hydraulic principles apply. The tricky part is to recognize and break down each part that needs to be figured.
Question: Two 2½-inch hoselines, each 400 feet long, are laid
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to a monitor that is 30 feet above the pumper. The monitor has
a 1½-inch smooth bore tip. What is the pump discharge pressure?
Answer:NP + FL + APP + ELEV
NP = 80 (Master Stream)
FL = 2Q2+Q
FL = 2(3)2+3
FL = 21/100 ft
FL = 84
APP = 10
ELEV = 30 × 0.434
ELEV = 13
80 + 84 + 10 + 13 = 187 psi
Question: You are supplying a ladderpipe that has a 1¾- inch
nozzle and is elevated 80 feet. You supply the ladderpipe with two
2½-inch hoselines that are 200 feet long. (Hint: 100 feet of threeinch hose is laid up the ladder.)
Answer:NP + FL (2½”) + FL (3”) + APP + ELEV
NP = 80
FL (2½”) = 2Q2+Q
FL = 2(4.1)2+4.1
FL = 2 x 16.81 +4.1
FL = 37.72 (38) x 2 = 76
FL (3”) = CQ2L
FL = .80 x 8.142 ×1
FL = 53
APP = 20 (ladderpipe + siamese)
ELEV = 80 × .434
ELEV = 34.72
80 + 76 + 53 + 20 + 34.72 = 263.72 psi
That’s it! That is the formula every pump operator needs to calculate each time a hoseline is laid. For new operators and even old timers who don’t practice every day, it is good to write the formula down
each time a hoseline is pulled and plug in the numbers. If a number
is written down for each value, the problem becomes a simple addition and subtraction problem. Sometimes more than one figure
needs to be put in for each part—for example, there might be two or
more friction loss figures. If the formula is written out, it is easier not
to forget a calculation. Many of these calculations can be figured out
ahead of time, written on a pump chart, and placed on the apparatus
near the pump panel. The most important thing is to practice so there
won’t be any problems when you are needed at a fire. ●
EndnoteS
1. John R. Freeman (1855-1932) was a civil engineer who was actively involved
in fire protection and reducing the insurance costs of fire. His papers “Experiments Relating to the Hydraulics of Fire Streams” and “The Nozzle as an
Accurate Water Meter” won awards from the American Society of Civil Engineers. His full biography is available on the Web at the Boston Society of Civil
Engineers Section, www.bsces.org/index.cfm/page/Biography/pid/10709.
2. Isman, Warren E. Fire Service Pump Operator’s Handbook. (Tulsa, Okla.:
Fire Engineering). 1984. Page 48.
● PAUL SPURGEON is a 20-year veteran of the Denver
(CO) Fire Department. Promoted to engineer in 1998, he
was assigned to Engine 7 in northwest Denver. He has
earned an AAS degree in fire science and technology from
Red Rocks Community College. He has authored Fire Service Hydraulics and Pump Operations (Fire Engineering).
Continuing Education
Every Pump Operator’s Basic Equation
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COURSE EXAMINATION
1)What is the basic equation used to calculate fire streams?
a.EP=NP+FL+HP+ELEV
b.EP=NP+FL+APP+ELEV
c.EP=HP+NP+FL+ELEV+APP
d.EP=FL+NP+ELEV+APP+Fog/Smoothbore
2)All figures used to calculate engine pressure must be used to
develop a proper fire stream
a.True
b.False
9)It is not the pressure of a stream that extinguishes a fire, but the
amount of water in gpm that cools a fire
a.True
b.False
3)If more than one size of hose is used, you must:
a. Figure
b.Figure
c. Figure
d.Figure
8)A _________is simply a tube that narrows down to an opening
with a specific inside diameter
a. Fog nozzle
b.Combination nozzle
c. Distributor nozzle
d.Smoothbore nozzle
friction
friction
friction
friction
loss
loss
loss
loss
for
for
for
for
each size
only one size
the longest hoseline
the largest size only
4)To be called a fire stream, a hoseline needs to have a nozzle
attached to its end
a.True
b.False
5)A discharge that is too weak:
a. May still provide enough water
b.May cause pump cavitation
c. May not be delivering enough water to overcome the British
Thermal Units (BTUS) being produced by the fire
d.May require smaller diameter hose
6)After water leaves the nozzle, the stream is also affected by:
a. Gravity and wind
b.Air and velocity
c. Elevation and gravity
d.Gravity and velocity
7)The fire service uses three standard nozzle pressures for smoothbore handlines, fog nozzle handlines and smoothbore master
streams. These pressures are:
a. 50psi, 150psi and 75 psi, respectively
b.100psi, 80psi and 50 psi, respectively
c. 50psi, 100psi and 80 psi, respectively
d.All operate at 50 psi
10) As a general rule, the maximum nozzle diameter should not
exceed __________of the size of the hose to which it is attached
a.Twice
b.Three times
c.One-half
d.Three-quarters
11) An advantage of fog nozzles’ ability to produce tiny water
droplets is:
a. Will absorb the heat faster than a solid stream
b.Apply droplets to more areas of the room
c.Assists with protecting firefighters from flashover
d.There is no advantage to tiny water droplets
12) Which attach method has the advantage of using relatively small
amounts of water?
a. Combination attack
b.Indirect attack
c.Transitional attack
d.Direct attack
13) The indirect attack is used only in enclosed spaces where there
is no possibility of life in the room
a.True
b.False
14) \What is defined as the loss of energy in pressure whenever
water runs though hose, fittings and appliances?
a.Head pressure
b.Static pressure
c. Friction loss
d.Elevation loss
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Continuing Education
Every Pump Operator’s Basic Equation
15) What are the two ways water flows through hoses?
18) Friction loss is governed by which of the following rules:
a. Laminar and metric flow
b.Laminar and turbulent
c.Turbulent and parallel
d.Parallel and laminar
a. Friction loss varies with the quality of the hose
b.Friction loss varies directly with the length of the hose
c. Friction loss varies with the square of the velocity
d.All of the above
16) I n _________ flow, the water flows in parallel lines with the flow
at the center moving at a greater velocity than at the edges, and
decreases the further out towards the edges of the hose
a.Turbulent
b.Parallel
c.Metric
d.Laminar
17) As water contacts the edges of the hose lining, coupling or a
bend, it causes
a.Friction
b.Laminar flow
c. Rub turbulence
d.Loss of water
19) What are two friction loss formulas commonly used by fire
departments?
a.Underwriter’s Formula and National Fire Academy Formula (NFA)
b.Underwriter’s Formula and Combination Formula
c.Underwriter’s Formula and Coefficient Formula
d.Coefficient Formula and NFA Formula
20) Water pressure will increase by .434 pound-per-foot increase
in elevation which is why pump operators must adjust for this
pressure
a.True
b.False
Notes
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Continuing Education
Every Pump Operator’s Basic Equation
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